INTERFERENCE OF LIGHT AND SOME METHODS 
OF MEASUREMENT 


BY 


THERON BAYNE CHANEY 
B. S. Knox College, 1921 


THESIS 


SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS 
FOR THE DEGREE OF MASTER OF SCIENCE IN PHYSICS 

IN THE GRADUATE SCHOOL OF THE UNIVERSITY 

OF ILLINOIS, 1922 


URBANA, ILLINOIS 


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UNIVERSITY OF ILLINOIS 


THE GRADUATE SCHOOL 


JUNE aia 192_< 


[ HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY 
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ENTITLED_INTERFERENCRP OF LIGHT AND SOuRr METHODS 
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TABLE OF CONTENTS. 


The numbers refer to pages, 


Foreword, 

£, Historical, 

II, The Meaning Of The Wave Theory. 

III. The Experiments Of Young And Fresnel. 

IV. Interference By Thin Films. 
Newton's Rings. 

V. Colors Of Thick Plates. Brewster's Bands, 

VI. The Michelson Interferometer. 

VII. Some Actual Experiments Using The Interferometer. 
1. Adjustment of the interferometer. 
2, Measurement of the wave length of sodium light. 
3. Ratio of the wave length of the D lines. 
4, Measurement of tne index of refraction. 

VIII. Some Famous Classical Experiments, 

IX, Other Types Of Interferometers. 
1, The Fabry-Perot Interferometer, 


2, Jamin's Refractometer. 


3. Lodge's Interferometer. 


x, Gonciusion. 


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INTERFERENCE OF LIGHT 
and 


SOME METHODS OF MEASUREMENT 
| 


FOREWORD 


In preparing this thesis, the writer has had two objects in 


2 ere 


mind, The first one was to enlarge his own knowledge of the sub- 
ject of interference of light waves. 

The second one was due to the writer's interest in the field 
of high school teaching. Ten of the most widely used textbooks 
in high school Physics were examined to see how much space was 
devoted to the subject of interference. Three of the ten made no 
mention of the subject. Two of them gave two and one half pages 
to interference, while the rest averaged about two pages. This 
thesis has been written therefore with the high school student 
in mind, and this has made it necessary to include considerable 
detail which might not have been included otherwise. It is hoped 
that this discussion will awaken in a few worthy students a live 
interest in the subject of interference and will encourage then 
to delve more deeply into this subject, one of the most fasci- 
nating in the field of Physics. If this hope is realized, the 
discussion will have justified itself. 


Digitized by the Internet Archive 
in 2015 


https://archive.org/details/interferenceofli00chan 


INTERFERENCE OF LIGHT 
and 


SOME METHODS OF MEASUREMENT 


This discussion will be considered under four heads as 


follows: 
A brief history o1 the development oz tne wave theory 


| 
{ 
of light contrasting it with the then prevailing theory of light | 
and including a short explanation of the theory. 

2. A description of tne experiments of Young and Fresnel and 
of other simple methods of producing interference of light lead- 
ing up to a description and explanation of the Michelson inter- 
ferometer. 

3. An account of some experiments performed by the writer 
with the Michelson interferometer together with a aescription of 
some of the practical applications and some of the classical ex- 
periments in which this instrument has been used, 

4, A description or some other well known types of inter- 
ferometer including some of the most important applications which 
have been made oI them. 

I, Historical. 

There have been a number of theories of the nature of light 


and the mode of its propagation from the time of the ancient 


Greeks down to modern times. Some of them were the result of much 
logical reasoning and withstood attacks from various philosophers 
for considerable lengths of time, Noteworthy among the modern 
theories of light was the corpuscular theory supported by Sir 


Isaac Newton, This theory postulated small luminous bodies which 


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were shot out in every direction from any luminous object, which, 


when they struck the retina of tne eye, produced the sensation of 
Sight. By making certain assumptions, this theory explained very 


satisfactorily the various phenomena which had been observed up 


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to that time. Because of this 1act, and aiso because of the great 
reputation of Newton as a scientist, this theory held its ground 
for a much longer time than it could have otherwise, 

But tue fact that new assumptions had to be made to explain 


newly observed phenomena with the corpuscular theory made it more 


Se 


or less unsatisfactory, and the undulatory or wave theory of light | 
as developed by Huyghens was advanced in opposition to the older ) 
theory of Newton. This theory provided very satisfactory explan- 
ations of various phenomena without the necessity of making the 
assumptions which often nad to be made with the other theory. For 
some time, there was considerable controversy over the relative 
merits of the two theories, and some very famous experiments were 
performed in an attempt to prove the superiority of one or the 
other of these theories. 

Assuming the corpuscular theory to be correct, it became 
necessary to suppose that lignt traveled taster in a denser med- 
ium such as glass or water than in a rarer medium such as air, 

Jusu tne reverse of this was true with une wave theory. An ingen- 
fous experiment by Foucault proved quite conclusively tnat light 
traveled with a siower velocity in water than in air. The result 
of this experiment provided strong proof ior the wave theory, but | 
in spite of it, the corpuscular tneory remained much in favor 

long after Newton's time. About a century later, Thomas Young 
Showed the interterence of light, and his work together with that | 


of Fresnel was une final blow which completely discreaited the 


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corpuscular theory, 

II. The Meaning of The Wave Theory. 

Before discussing the work of Young and Fresnel, some con- 
Sideration must be given to the meaning of tne wave vheory of 


light. For our purpose, we may define a wave as a progressive 


| 
| 
Shape or torm which is propagated through a medium by tne regular i 
periodic vibrations of the particles of which the medium is com- | 
posed, Every one is familiar with the waves wnich travel across | 
the surface of still water when it is disturbed. Knergy is trans- | 
Miuted along the surtace of the water py the waves, but tne water 
itself aoes not move with tnem. Instead, the particles ot water 


execute an oscillating motion as each wave passes by. Waves may 


also be illustrated by a rope which is attached to a rixed body 
at one end, the other end being held by the hand. If the hand is 
movea periodicaliy up and down, waves will pass along the rope 
from the hand to the rixed end. These waves will be executed in a 
vertical plane when the hana 18 moveu in a vertical line, and the 
energy which the waves carry aiong may be felt by grasping the 


rope firmly at tne fixed end. 


Ww x 7 
Figure 1, 
Let Figure 1 represent the waves which travel along the rope, | 
The points a, b, c, d, etc. are know as the crests of tne waves, 
and the poinus w, x, y, 2, etc, are called the troughs. Consider- 
ing that une wave is traveling from left to right, let b repre- 
sent a small section of the rope at the crest of a wave. An in- 


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the trough w will now be immediately under the point where the 
crest was tne preceding instant. But the section b of the rope 


has not moved forward, but has moved downward. An instant later, 


of the rope is oscillating in a vertical line which is perpen- 
dicular to the direction of motion of the wave. The wave AE there- | 
fore advanced by the oscillation of many sections of the rope, 
each one vibrating in a line perpendicular to the direction of the 
wave motion, and each one passing its motion on to the next sec- 
tion. It is important to note here that the energy transmitted to 
the rope by the hand is carried forward wholly by the wave itself, 
the sections of tne rope retaining their relative positions 
throughout, 

The wave theory of light is very aptly illustrated by the 
analogy of the rope waves given above, Light is a form of energy 
which is transferred by wave motion just as the energy which is 
communicated by the hand to the rope was transferred from one end 
of the rope to the other by the rope waves. But the rope waves 
have a visible medium by means of which they move forward, which 
is the rope itself, each section of the rope vibrating period- 
ically in a line perpendicular to the direction of wave trans- 
mission. As far as the eye can tell, there is no such medium by 
which light waves may be transferred, but we know that it is 
transmitted through the air as well as through space in which 
there is no air, Obviously, if light consists of wave motion, 


there must be a medium filling all space which will transmit 


these waves, Such a medium is assumed to exist, although its 


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existence cannot be proved, and this medium is calied the ether. 
It fills all space not occupied by other forms of matter. It is 
necessary to assume certain properties for the ether which are 


quite paradoxical, It must be a perfectly frictionless fluid nel 


will offer less resistance to a body passing through it than the 


lightest known gas, But when a force is exerted upon a gas and 


| 
| 
i 
Some of the molecules are displaced from their original positions, | 
they do not return uo the original position when the force is re- | 
moved, But in the case of wave motion, the particles must return | 
to their position. Hence the ether must have great elasticity. 
Indeed, it is often spoken of as an elastic solid with the seen- 
ingly impossible property of being frictionless as already stated 
above, This then is the medium by which light energy is trans- 
ferred as wave motion. As the light wave passes through the ether, 
each particle executes a periodic vibration perpendicular to the 
direction of motion of the wave in the same manner as each section 
of rope in a rope wave. Thus the light wave passes through the 
ether without the forward motion of the individual particles. 
This constitutes one of the main points of departure from the 
corpuscular theory. In this theory, the light energy is carried 
forward by small particles themselves, the particle actually mov- 
ing forward in the direction of motion of the light ray. 


Let us return for a moment to the analogy of the rope waves. 


Let Figure 2 represent the waves passing along the rope, The 


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Figure 2. 


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distance from any crest x to the line AB is equal to the perpen- 
dicular distance from any trough y to the line AB, This distance 

represents the maximum displacement which a section or particle of 
the rope undergoes as the wave passes along the rope. This is the 
amplitude of the wave, The distance from any crest to the adjacent | 
crest 1s one wave length, likewise from one trough to the next, 
The time taken for one wave length to pass a given point is the 


period. The portion of the wave through which a given particle 


ATE Eo SEE 


ST 


has vibrated at the end of a certain time is called the phase, 
Any two particles which are separated from each other by a dis- 
tance equal to half a wave length are in opposite phase. Thus 
consider two particles m and n as shown in Figure 2, They are a 
half wave length apart and are in opposite phase. If m is moving 
upward, then n is moving downward, Similarly, the points p and 

q are in opposite phase being separated from each other by a 
half wave length, But the points p and r are a whole wave lengtn 
apart, hence they are in the same phase, 

Suppose that at time = 0, a source of wave motion begins 
sending out waves, At the end of one second, it will have sent 
out N waves, and if each wave has a length 1, the distance which 
the N waves will fill will be Nl. This means that the first wave 
will have traversed a distance equal to Nl in one second, and it 
will continue to do so in the succeeding seconds, This is the 
velocity v of the wave, and we may say that 

ee OR (1) 

Let us now consider for a moment waves on the surface of 

water, As the waves travel over the water, the particles of water || 


take on an oscillating motion but do not move forward with the 


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wave, Suppose that we have waves coming from two sources A and B 

on the surface, They will spread out in all directions as shown in 

Figure 3. Let the waves from both sources have the same wave 
length, the same amplitude, and 
the same velocity. In the figure, 


the continuous lines represent 


Zo on SAE Ww aN 
Les SRK See SS . wave crests, and the broken lines | 
Vi 7, wi ED SAO 
/ Wi fpges MXN Ares WW \ represent wave troughs, At the 
Ag ~ | BS \ 1 
if, VAN AWN 
bo eiiah aa Ma VNU speintex, two crests’ from the dir. | 


| 
| 
| 
| 
i 
| 
Figure 3, ferent sources meet. Hence the 
waves at this point are in the same phase, and the oscillating 
particles of the water take up energy from both waves so that its 
displacement is equal to the sum of the displacements which would 
be caused by either wave acting alone. Therefore, the crest will 
be higher here than the crest of either of the individual waves, 
Similarly, at the point y, two troughs are together, and the dis- 
placement of the water particles at this point is equal to the 


sum of the displacements caused by the two waves acting alone, so 


that the trough is deeper. 


Now let us see what happens at the point w where the crest 


of one wave meets the trough of the other. From our definition of 
phase as applied to rope waves on page 6, it is seen that these | 
two waves are in opposite phase. Therefore the motion of one of i 
the waves will tend to cause a displacement of the water parttoles 
in one direction, while the motion of the other wave will tend to 
produce a displacement in the opposite direction, The resultant 
displacement, being the sum of the two displacements of the two 


waves, will be zero since the motions of the two waves oppose or 


Pe . 

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annul each other, Hence the particles of the water will not move 


in either direction, and the surface of the water will remain 


quiet. From the figure, it 1s seen that there are other points 

besides the point w at which waves in opposite phase meet, and 
lines have been drawn through these points. These lines represent | 
regions where the water is smooth and quiet, while between these | 
lines are regions of maximum disturbance, When the waves meet eues| 
in opposite phase, they are said to interrere with each other, a 
this phenomenon is known as interference. In contrast to this, | 
the waves which meet in like phase are said to reinforce each oth- | 
er, | 

III. The Experiments of Young and Fresnel. 

Sir Thomas Young proved the wave theory of light to be the 
correct one beyond all doubt when he showed the phenomenon of the 
interference of light. He knew that if light is propagated by 
wave motion, tnat there should be interference of the light waves 
under proper conditions, He therefore made some very famous, yet 
very simple experiments which proved his theory to be correct. 
One of his most noted experiments was as follows: He allowed 
light streaming through a very 
narrow slit S, (Figure 4) to fall | 
upon two other narrow slits A 
and B which were parallel to the 


slit S, and were very close to 


each other. The slits are shown 
Figure 4, in the figure as being perpen- 
dicular to the plane of tne paper, After passing through the slits) 


A and B, the light was aitloweda to fall upon the screen PQ, and 


on this screen, 


= 


tue phenomenon of interference was observed. To 


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@ show more clearly what took place, let A 


p and B in Figure 5 represent tne two slits 


c through which the light passed, The light 


qi in the same phase as that which passes 


| | p which passes through A at any instant is 
| Figure 5, d through B at the same instant, Let the 
i 


light from tne two sources meet on the screen XY at the point P, | 


and Suppose that the distance BP which the light which passes 


through B has traveled, is longer than the other path AP by half 
a wave length, Then these two wave trains will be in opposite 
phase at the point P and will therefore interfere with each other, 


Assuming that the light is of one single pure color, in other 


[SEES RT AOS OR 


SE I SR TEE ESI 
SE PS eres wore oneuernnn awanwnnrnorann eauy nase asnonennenes 


words, monochromatic or of a single wave length, there will bea 
dark band on the screen which is parallel to the slits A and B 
and which passes tnrough the point P. Now consider the point C. It 


which is perpendicular to the plane in which the slits lie. There- 
fore C is equidistant from A and B, and wave trains of light from 
these siits will arrive at C in tne same phase, and there will be 
reinforcement so that there will be a bright band through this 


| lies upon a line which is half way between the slits A and B and 
point, By similar reasoning, it can be shown that there will be 


SRR Seer 


= Se 


another dark band at P' which is on the opposite side of C from 
P. Now let us consider two more wave trains passing out from A 


and B along tne paths AQ and BQ, and let BQ be longer than AQ by 


of half wave lengths, Then at this point, the two wave trains will 


| 
i 
a whole wave length, or what is the same thing, by an even number | 
i 
reinforce each other, and there will be a bright band passing | 


through Q. By similar reasoning, it may be shown that there will 


also be a bright band on the opposite side of © at Q'. Thus we 


will have alternate bands of interference 


and reinforcement on the screen, and the 


| Figure 6. These alternate bright and 


field will resemble the illustration in : 
| 


Figure 6, dark bands are called interference || 
fringes. This phenomenon may perhaps be made somewhat clearer by 
studying the geometry of Figure 7. Let P be a point on the screen 
such that the distance AP 
is n half wave lengths great- 
er than the distance BP, or 


if 1 = the wave length, 


Figure 7. AP - BP=nd (2) 

Let the distance MP = x, and let OM = a. Then with P as the cen- 
ter and with PB as the radius, draw the arc BC. Since in the ac- 
tual experiment, the slits A and B are very close togevher con- 
pared to the distance PB, the arc BC will be approximately a 
straight line perpendicular to OP. Now AB is perpendicular to OM, 
so that we have two angles ABC and MOP, which are equal, because 
the sides of one are perpendicular to the corresponding sides of 
the other, Since these angles are equal, the two right triangles 
ABC and MOP are similar to each other. Then we may say 

RM. aC - 2 = (3) 

Ot BE AB 
Since AB is very nearly equal to BC. Let AB = c, AC is the dif- 


ference between AP and BP which has been shown above in (2) to 


equal nl/2. Therefore 


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This equation gives the distance x which any fringe may be from 
the point M on the screen which lies on the perpendicular bisec- 
tor of AB. Now suppose that in equation (5) n = 0. Then the whole 
right hand side of the equation is equal to zero or x = 0. This 
means that the difference in length of the paths AP and BP has 
become zero, and the point P will now coincide with M. Light waves | 
coming trom the two sources A and B will therefore be in the same 
phase when they meet at M, and there will be a bright fringe or 
band on the screen passing through M. This is called tne central 
fringe. We have already seen that when the difference in path of 
the two wave trains is equal to an odd number of half wave lengths | 
that the waves will be in opposite phase and will therefore cause | 
a dark fringe. Therefore when n in (5) is an odd number, x will 
be the distance of the nth fringe from the central fringe, and | 
this fringe will be dark. Likewise, if n is an even number, x will | 
be the distance of a bright fringe from the central fringe, and 
it will be n fringes from the central one counting both bright 
and dark fringes, Tnis reasoning holds good tor light of a single 
wave length, 

Suppose that we have white light which is made up of the 
various colors of the rainbow, or more correctly, the spectrun, 
From equation (5), it is seen that the distance x is proportional 
to the wave length 1. Let n be an even number so that P (Fig. 7) 
will be a bright fringe. Now the wave length of red light is much 
longer than that of violet light. If we substitute the wave 
length of red light for 1 in (5), it is seen that the distance x 


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will be greater than it would be if the shorter wave length of 
violet light were substituted for 1, Hence the fringe will vary in| 
color from the red to the violet of the spectrum, and the violet 
edge of the fringe will be nearer to the central fringe than the 
red edge, because the violet wave length is shorter, Therefore for | 
white light, instead of having bright and dark fringes as in the 
case of monochromatic light, we have rainbow colored fringes sep- 
arated by dark spaces, the inner edge of each fringe being violet 
and the outer edge being red, The other colors of the spectrum 
whose wave lengths lie between those of the red and violet will 
also be seen in the fringe, each merging gradually into the other. 

The explanation of Young's simple experiment here has been 
dwelt upon at some length, because it furnishes a foundation for 
understanding other applications of the principle of interference, 
It should be noted from this explanation that in order to produce 
interference, there should be two sources of homogeneous light, 
the light proceeding from cach source in exactly the same phase, 
The slits A and B in Figure 4 are considered as sources, so the 
light which falls upon A and B must come from the same primary 
source, such as S, so that the waves proceeding from A and B may 
be exactly alike at any given instant. It should be mentioned here 
that Grimaldi tried this same experiment about 150 years before | 
the time of Young, He made the mistake of allowing the light to 
fall directly upon the slits A and B without first passing it 
through the slit S. Hence the light which passed through A and B 
was not homogeneous, and he failed to observe true interference 
of light. In addition to having homogeneous light, there must 


also be a difference in path of any two wave trains passing from 


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A and B to a point P equal to an even number of half wave lengths 
for a bright fringe or to an oda number of half wave lengths for 
a dark fringe, These are the condivions necessary for interference. 
Besides Sir Thomas Young, the other great physicist whose 
name is most intimately connected with the principle of interfer- 
ence in its early development is Fresnel, a Frenchman. Fresnel 
produced interference fringes in over at different ways, two of 
which will be ex- | 
plainea nere. In 
the first method 
described here, he 
used two plane mir- 
rors inclined to 


each other at an 


Figure 8, angle of nearly 
180 degrees, so that they almost lay in the same plane as shown 
in Figure 8, ON and OM are the two mirrors. S is a source of light 
in the form of a narrow slit which is parallel to the dividing 
line between the two mirrors. The light from S which strikes ON 
is reflected toward the screen PQ as if it originated at the point 
B which is really the reflected image of the luminous slit in the 
Mirror ON, Light which strikes OM is also reflected to the screen 
PQ aS if it originated at the point A which is the reflected 
image of the slit in the mirror OM. It is seen that the light 
trom the two virtual sources A and B, overlaps in the shaded por- 
tion just the same as the light overlapped from the two slits A 
and B in Young's experiment, (Fig. 4). Therefore tne area DE of 


the screen covered by these overlapping fields of lignt will be 


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crossed by interference fringes. In this, as in Young's experiment, 
we have two sources of light A and B, and we know that the light 
waves proceeding from these two sources at any given instant are 
in the same phase, because the sources are images of the real 
source of homogeneous lignt. sane Besa on tae screen between 
D and E are at difrerent distances from A and B, so that at some 
points, bright fringes will appear while at others, there will be 
dark bands, 

Fresnel produced interference in another manner by means of 
what has since been known as the Fresnel Bi-prism. The bi-prisa 
is illustrated in Figure 9. It consists of two glass prisms 
placed together base 
to base at E, The 
angles at C and D 
are very small so 
that the angle at E 
is very nearly a 


straight angle, 


Figure 9. Light from a slit S 
falls upon the back of tne two prisms, That which falls upon the 


upper prism is refracted downward and proceeds to the screen PQ 


as if coming from a source S&:. That which passes through the 


lower prism is refracted upward and proceeds to the screen as if 
coming from a source S22. It is seen that the diverging beams from 
these two virtual sources overlap each other as shown in the shad- 
ed area of the figure, and where these overlapping beams strike 
the screen, fringes will be formed. These two methods of Fresnel 
were an advance over Young's experiment, because they provided 


two sources of light very close together without the aid of any 


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apertures or sharp edges which might cause other effects besides 
interference, In fact, some of Young's contemporaries rather 
doubted his conclusions, because he used the two slits or aper- 


tures having sharp edges. It had already been observed that light, 


passing through a very small opening or past sharp edges, was 
ditrracted, forming tringes very similar to interference fringes, | 
and it was tnought by some that Young had opserved this diffrac- 
tion effect instead of true interference. But Fresnel‘s work with | 
his mirrors and bi-prism showed quite clearly that Young's con- | 
Clusion was correct, and that he had actually obtained interfer- 
ence fringes, 

Mention should also be made of a method of producing inter- 
ference fringes due to Dr. Lloyd of Trinity College, Dublin. This 
method is known as Lloyd's 
Single mirror method and 
was first described by 
him in 1834. A long, high- 
ly polished mirror is used!) 


(Pig. 10). Light, from a 


Figure 10. source S in tne form of 
a narrow slit, is allowed to fall upon the mirror at almost a 


grazing angle, that is, the angle of incidence is very nearly 


ninety degrees, It is then reflected in a diverging beam towards 


the screen PQ as if it originated at a point 8:1, which is the 
reflected image of S in the mirror, Light coming directly from 
the source also strikes the screen, and the two beams overlap 
each other as shown by the shaded area, Hence these two overlap- 


ping beams produce interference fringes on the screen in the. 


-prisn., || 


same manner as they are produced by Fresnel's mirrors or bi 


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IV. Interference By Thin Films. 
We shall now take up briefly a study of the colors produced 

by very thin films, these colors being formed by interference of 

light waves, The following experiment will aid in understanding 

this phenomenon, Take two pieces of 


optically plane glass which have been 


carefully cleaned and are free.from 


dust, and both of which are one or 


two inches wide and four or five in- 


ches long. Lay one piece on the oth- 


Al ep er and clamp them together loosely 
| 


Figure 11, firmly. (Fig. 11). Then we have a 


at one end. Between the two plates 
at the opposite end, place a single 
silk fiber or a bit of tissue paper, 


and pressthe two plates together 


very thin wedge of air between the two plates. The figure is very 


much magnified in order to show the principle more clearly. It 


is seen that the air wedge widens at a constant rate from the top 


to the bottom. Let S be a source of monochromatic light such as 


a sodium flame. Light proceeding from this source will strike the 


glass and some of it will pass clear through both plates, while 


some of it will be reflected from each of the four surfaces. In 


this experiment we are concerned only with the light which is re- 


flected from the two inner surfaces, AB and AC. Hence there will 


be two wave trains of light superposed upon one another which are 


reflected from AB and AC in the direction OP. Now from an inspec- 


tion of the figure, it is seen that the wave train which is re- 


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flected from the surface AB, has traveled a greater distance than 
the wave train which is reflected from AC. If this difference in 
path is such as to make the two emerging wave trains in opposite 
phase, they will annul each other, and a dark band will be seen 
across the plate at this point. On the other hand, if the differ- 
ence in path of the two wave trains is such that they emerge in 


the same phase, they will reinforce each other, and a bright | 
fringe will be seen on the plate. Now we know that for two wave 


trains to interfere with each other, there must be a retardation 
of pace au ena the otaer by a half wave length, or an odd number 
of half wave lengths, so that they will be in opposite phase. 
Hence it would seem that interference would take place at a point 
where the distance through the air wedge and back is a half wave 
length or an odd number of half wave lengths. Likewise, for re- 
inforcement, the distance through the wedge and back should be 

a@ whole wave length or an even number of half wave lengths, But 
just the opposite of this is found to be the case, Why this should | 
be so is easily explained, It is a well known fact that when light 
waves, passing through a given medium, air for example, strike a 
denser reflecting medium such as glass, they suffer a change in 
phase of a half period upon reflection. That is, a crest of a 
wave will be reflected back as a trough and vice versa. But if the | 
wave train is passing through glass and is reflected back from a 
rarer medium such as air, it will not suffer this change in phase. | 
Now suppose that the distance through the air wedge and back at 
the point M (Fig. 11) is one half of a wave length. This will re- 
tard the wave train reflected trom AB one half wave length be- 
hind the train reflected from AC, But the wave train reflected 


from AC is reflected from an air surface which is rarer than the 


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glass which it has just passed through and therefore suffers no 
change in phase. The other wave train has been reflected from a 
glass surface after passing through the air wedge, so that it has 
undergone a change in phase of half a period. This change added 
to that produced by the thickness of the air wedge retards this 


wave train one whole wave length behind the other one, so that 


| 
they both emerge from the plate in the same phase and reinforce | 
each other, Now consider a point N (Figure 11) farther down the | 
air wedge where the thickness through the wedge and back is one | 
whole wave length. Then one wave train will be retarded behind the | 
other by a wave length, but as in the case above, it will also i 
undergo a change of phase of half a period so that it will emerge 
from the glass one and one half wave lengths behind the first 
wave train and will thus interfere with it because it is in op- 
posite phase, Therefore, we must conclude that where a dark band 
is geen across the plate that the distance through the wedge and 
back is at least one wave length or an even number of half wave 
lengths, Likewise, where a bright band is seen, the distance 
through the wedge and back will be at least a half wave length or 
an odd number of half wave lengths. When the light falls perpen- 
dicularly upon the first plate, the distance through the air 
wedge may be expressed as 

a nedel (6) 
For light which does not fall perpendicularly upon the plate, the 
above equation is only approximately true. In such a case, the 
accurate expression involves a trigonometric tunction of the 
angle df incidence, Equation (6) gives the distance which the 
wave train travels in passing through the air:wedge and back 


again, Clearly then, the thickness t of the wedge is one half 


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t= —g— = B- (7) 


In equation (7), 1 18 the wave length, and when n is an even nun- 


{ 


ber, the expression gives the thickness of the wedge at a point 
where interference takes place, When N is odd, t will be deter- 
mined tor a point where reinforcement takes place, Since the air 
wedge widens at a constant rate, it is evident that tnere will be 
a number of points between the top and the bottom of the wedge 
where interference and reinforcement will alternately take place. 
n for any particular fringe will be its number from the top of 
the wedge down counting both dark and bright fringes. Thus for 
the first, second, third, etc., bright fringes, n will be equal 
to 1, 3, 5, ete., and for the first, second, third, etc., dark 
fringes, n will be equal to 0, 2, 4, 6, etc. This experiment is 
not very hard to perform, and the fringes may be easily seen with 
the naked eye if the eye is in such a position as to receive the 
light reflected from the plates, The experiment is very inter- 
esting and very instructive, 

It has been assumed thus far that in this experiment, light 
of only one color is used as tne light trom the sodium flame. 
Suppose that white light is allowed to fall upon the plates, Then 
a series of rainbow colored fringes will be seen separated by 
dark bands or fringes, Let us consider one of the bright fringes 
for which n in equation (7) will be an odd number, Then for this 
particular fringe, n is a constant, and 1 is the only variable. 
The thickness t will therefore be proportional to 1. Since the 
fringe has width, it follows that t will be greater at the bot- 


tom edge of the fringe than at the top. Therefore the wave length 


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of tne light which is seen at the bottom edge of the fringe must 
be longer than that of the light at the top edge of the fringe. 
It will be observed that the lower edge of the fringe is red while | 
the upper edge is violet. This furnishes proof therefore that the 
|; red end of the spectrum has longer wave length than the violet 
| end. Another way of showing this is to interpose a piece of red 
| glass between the source of white light and the plates. Thus only 
| red light will fall upon the plates and only red fringes will be 
seen with dark bands between each two, Tne number of fringes, 
both bright and dark, should be counted, and their distance apart 
should be observed. Now interppose a piece of blue or green glass 
between the source and the plates. Blue fringes will now be seen, 
or green ones as the case may be, and it will be observed that 
they are closer together, and that there are more of them than 
for red light. This shows then, that the wave length of either the | 
blue or the green light is shorter than that of the red. 

With this simple piece of apparatus and by use of equation 
(7), the wave length of monochromatic light may be roughly ap- 
proximated. Let tne plates be illuminated with yellow light from 
a sodium flame, Count the number of fringes from the top to the 
bottom of the plates, both dark and bright ones. This will give 
n of equation (7). Then with a micrometer microscope, measure the 
thickness of the base of une air wedge. This will be t. We may 
substitute uhnese observed values in tne equation and solve for 
1, tne wave length. Let us suppose tuat the number of fringes 
counted is 24, and that the thickness of tne wedge was found to 
be ,0035 millimeter. Substituving vuhese values in equation (7), 


we have NAM te 8 61 


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ane 6 = ,000583 millimeter 


which is a fairly close value for the wave length of sodium light 
considering the crudity of the apparatus. 
Considerable space has been given to the explanation of this 


Simple piece of apparatus, because it furnishes the explanation 


cer 


to many phenomena which we see everyday. A very simple experiment 


which any one can do is as follows: Take a piece of wire and bend 


it into a small loop with a handle at one side. Dip the wire into 


&@ prepared soap solution, and on taking out, a soap film will be 


stretched across the wire loop. At first, the film will be of uni- | 


form thickness throughout, but if held vertically, the liquid in 


the film will run down to the base, so that the thickness of the 


film will increase toward the bottom. Thus we have a wedge of the 


soap solution instead of a wedge of air, and light will be re- 


flected from both surfaces of the film causing interference to 


take place, White light thus reflected will be seen as very beau- 


tiful colors varying from the red to the violet end of the spec- 


trum. As the liquid of the film is constantly draining to the 


bottom, the positions of the colors will be changing continuously 


which adds much to the beauty of the effect. As the top of the 


film gets thinner and thinner, it will eventually become black. 


When the black area appears, the film is so thin that it soon 
breaks. In fact, it is so thin that the distance through it and 


back is practically zero, so that there is no retardation of one 


wave train behind the other. But one wave train is reflected from 


a denser medium than that through which it has passed, so that it | 


suffers a change of phase of half a period. The other wave train 


does not suffer this phase change, because it is. reflected from 


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@ rarer medium. Hence the two wave trains are in opposite phase 
and therefore interfere with each other thus producing the dark 
, region on the film. 

Thus far, the fringes which we have discussed which are pro- 
duced by thin films, have been straight fringes extending across 
the fiela of the film. A very simple experiment will show frimges 
produced in the same way which are circular, Take a piece of clean 
plate glass and lay it where light from the sky (not direct sun- 
light) will be reflected from it. Lay a thin piece of glass such 
as a microscopic cover glass upon the plate and then press down 
upon the center of the cover glass with the point of a needle or 
apin. A very slight pressure is all that is needed to produce 
Circular colored fringes with the pin point as the common center 


of the circles. If there are slight irregularities in the surface 


be closed curves. Sir Isaac Newton made a very complete study of 


such fringes, and they are therefore known as Newton's rings. He 


of curvature, upon a plate 


of glass. The lens touched 


C, Now the lens diverges away from the plate at all points from 
the center out to the edge. Thus we have what might be termed a 
circular air wedge. The loci of ali points on the curved surface 
of the lens, which are equidistant from the plate, are circles. 
Let light from a source S fall upon the plane side of the lens. 
Some of it will pass through and will be reflected at the point P 


LEMS 


eee Fe 


Seen eee | 


of the glass, the fringes may not be truly circular, but they will | 


S; 4 ° produced these rings by lay- | 
ing a convex lens, (Fig. 12) | 


which had a very long radius | 


Figure 12, tne glass plate at the point | 


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on the convex surface of the lens. Part of the light will also | 


pass on to the plateand will be reflected at the point O of the 
plate. Both wave trains will be reflected in the direction 0Q. 
-As in figure 11, one wave train will travel a greater distance 


{ wa 
than the other, and if this distance is such as to cause the two 


waves to emerge from the lens at L in opposite phase, they will 
interfere with each other thus causing darkness. Now there will be 
a large number of pairs of points as O and P for which che dis- 
tance between each pair will be the same, and these points will 
all lie in a circle about C as the center. Hence there will be a 
dark ring caused by interference at all these points. Let us con- 
sider two points further out on tne lens and plate such as M and 
N. Here the distance between M and N will be such that the two 
wave trains will emerge from the plane surface of the lens at F 
in tne same phase and will therefore reinforce each other. Like- 
wise, we will have a circle of such points about C as a center 
where reinforcement will take place so that there will be a bright 
circular fringe. From tne center out to the edge then, there will 
be a number of bright and dark circular fringes. At the center, 
where the lens touches the plate, there will be a dark spot. This 
corresponds to the dark area seen in the thinnest part of the soap 
film just before it breaks. The rings nearer the center will be 
wider than those nearer the edge. This is due to the fact that as 
we get farther away from the center, the thickness of the wedge 
increases at a more rapid rate so that the points where inter- 
ference and reinforcement take place are closer together tnus 
making the rings narrower, Since the wave length of light at the 
red end of the spectrum is longer than at the violet end, the 


distance between uhe lens and the plate which will produce rein- 


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forcement of red light waves must be greater than for violet waves, 
Therefore the outer edge of each ring will be red and the inner 

edge will be violet with the other colors of uhe spectrum plending 
from one to the other between, It is interesting to note the ef- | 
fect of monochromatic light in producing Newton's rings. Red glass | 
may be interposed in the beam of light coming from the source, so 
that only red rings will be seen. Then if the red glass is removed | 
and blue glass is interposed, blue rings will be seen which have | 
shrunk toward the center and are not as wide as the red rings. 

This is due to the shorter wave length of the blue light. 

The number of rings which can be seen using white light is 
very small compared to the number wnich may be seen when mono- 
Chromatic light is used. This is due to tue fact that the red out- 
Side edge of one fringe tends to overlap the blue or violet inner 
edge of the next fringe which produces indistinctness, This over- 
lapping increases as we come closer to the edge of the lens , and 
as a@ result, the outer rings disappear entirely, With monochro- 
matic light, this overlapping is impossible, so that more rings 
will be seen. In his study of these rings, Newton found that the 
radii of the different rings for a given angle of incidence were 
proportional to the square root of the numbers 1, 2, 3, 4, ------ ; 
Thus the radius of the fourth ring is twice the radius of the 
first ring, and the radius of the ninth ring is three times the 
radius of the firsu ring. It should be emphasized that in all 
cases of interference produced by thin films, the character of the 
fringes varies greatly with the angle of incidence of the light 
falling upon the film and also with the index of refraction of the 
material of the film. Newton found the way in which the radii of 


the rings varied with the angle of incidence to a great degree 


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of accuracy considering the fact that he had very rough instru- 


ments to work with, He also made the first measurements of the 
wave length of lighu by the use of these rings, although he did 
not think ot his measurements as wave lengths, because he believed 
in the corpuscular theory of light. 

Newton's rings, as well as ouher interference bands, may also 
be seen by means of light which is transmitted through the plate 


| 
ana lens rather than reflected from them. In the case of reflec- | 
tion, as already mentioned, one of the wave trains suffere a | 
phase change of half a period while the other does not, pecause 


they are reflected from mediums of different densities, But when 


the light is transmitted clear through the lens and plate, there 
is no reflection, hence no change of phase in eitner wave train 
due to reflection, Therefore, wuere a bright ring is seen by re- 
flected light, a-dark one will be observed by transmitted light. 
The colors of the rings will be complementary to the colors of 
the rings seen by reflected light. The center of tne system will 
be marked by a bright spot instead of a dark one, and the red 
edge of each fringe will be on tne inner side of the ring instead 
of on the outer siae, Arago proved quite conclusively that the 
two systems of rings caused by transmitted and reflected lignt 
are complementary. He took a 
et” plate of glass and a convex 
lens and set them up as shown 
in Figure 13 on a sheet of 
uniformly iliuminated wnite 
Figure 13. paper. Light from the paper 
i. at any point B on the same side of whe plate and lens as the eye 


produced Newton's rings by reflection, Transmitted lignv from the | 


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opposite side, such as at point A, produced the rings by trans- 
mission. Since these two systems of rings were complementary to 
each other, Arago predicted tnat uniform illumination would re- 
Sult ir the field were viewed by reflected and transmitted light 
at the same time. His predictions were fully verified by the ac- 
tual experiment, 

Nature produces for us many very beautiful color eftects 
due to interference from thin films. One of the most common ex- 
amples 18 seen where there is a film of oil on the surface of 
water, Some of the light is reflected from the top surface of the 
oil film, while part of it is reflected from the lower surface, 
or the surface of the water. The oil film varies in thickness from | 
place to place, so that difrerent colors are reinforced at differ- 
ent parts ot the film. If a very smali drop of o1i1 is placed care- 
fully on the surface of very quiet water, it will spread out in 
the form ot a circular film, being tnickest at the center and 
gradually getting thinner towards the edges, It will thus pro- 
duce Newton's rings quite perfectly. Usually however, the oil is 
distributed over the surface quite irregularly, so that there is 
no regularity of color arrangement, 

Another example of this type of interference is often seen 
upon the surface of highly polished steel which has been exposed 
to the air for a few days so that a thin film of oxide has been 
formed upon it. The light is reflected from the surface of the 
film and also from the surface of the steel underneath, so that 
interference is produced, 

V. Colors Of Thick Plates. Brewster's Bands. 

Before taking up the theory of tne interferometer, it will 


aid in understanding it to consider briefly interference produced 


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by tnick plates, Sir David Brewster first made a study of this 
phase of the subject of interference in 1815. He used a device, 
the essential parts of which 


are shown in Figure 14, It con- 


2 A 4 sisted of a straight tube which 
was blackened on the inside, 
Figure 14, One end of the tube was closed 


except for a small opening 0, through which light could be admit- 
ted, At the other end of the tube were placed two glass plates of 
equal thickness. The plates were placed very close together, and 
one plate A was set so as to be at right angles to the tube, The 
plate B was inclined at a small angle to A, This angle could be 
varied by means of a micrometer screw. When a beam of light passed 
through 0, by looking in at the other end of the tube, Brewster 


observed interference fringes. The explanation of these fringes 


: is more easily seen by referring to Fig- 
ure 15. Light coming from the direction 
shown by the arrows passes through to 
the lower surface of the plate A, is re- 

leur 15. flected back to tne upper surface, and 


is again reflected downward passing out from A and directly 
through the plate B to the eye. A second wave train D passes di- 
rectly through A on into B, is reflected from the lower surface 
of B to the upper surface, thence back again and out to the eye. 
Now it is clear that if the two incident wave trains are in the 
same phase and are parallel to each other, and if both plates are 
parallel to each other and have the same thickness, then the 
length of path for both wave trains is exactly tne same, and they 


arrive at the eye in exactly the same phase causing reinforcement. | 


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But if the plate B is inclined to A at a small angle, the thick- 
ness of glass through which the wave trains pass in the plate B 
is slightly greater than in A. The path followed in tne reflec- 
tions between the surfaces for the wave train D is therefore a 
little greater than for the reflections of the wave train C in 
the plate A. Therefore, the wave train D is retarded behind C, and | 
they are thus in a condition to produce interference, Between two 
Such plates, there may be several different combinations of re- 


flected wave trains, all of wnich will produce interference. Fig- 
A 


ure 16 shows a few of tne con- 


Sie Se | a 


TATE 


2 ee el | ae ae 


binations which may take place, 


In Figure 15, the wave trains 


pass between the two plates 


Figure 16 only once. In Figure 16, the 
two sets of wave trains, A and B, pass between the plates three 
times, while tne set C passes between the plates five times. Each 
of these different combinations will produce a system of fringes, 
and if conditions are right, these different systems may be seen 
at the same time. Brewster's bands may be very easily seen by 
setting up @ simple apparatus 
a such as is shown in Figure 17. 
Take two small plates of glass 


and lay them, one on top of tue | 


other, on a dark surface, Prop 


up a piece of ground glass at 
Figure 17. one side of the plates and at 
an angle of about 45 degrees with the surface of the table, The 
ground glass diffuses the lignt which passes through it from a 
sodium flame. With the eye in the position indicated so as to see 


ious 


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1 BA 


the reflected light in the glass plates, a system of fringes will 


be seen on the field of light in the plates, These fringes may be 


eitner straight or curved. Since the plates are in contact with 


each other, their adjacent surfaces cannot be inclined to each 


other at an angle as suggested above in connection with Figures 


14 and 15. Hence the fringes must be due to the fact that one 


plate of glass is slightly thicker than the other, and any single 


fringe will be the locus of all points at which the thickness of 


one plate differs from that of the other by a constant amount. 


This fact is often made use of to test the trueness of surface of 


a plate of glass, It is often desired to determine the constancy 


of the thickness of a large sheet of glass. To do this, a small 


Square of glass is cut from the corner of the large sheet and laid 


upon the sheet. This is illuminated by a sodium flame, the light 


being incident at about forty five degrees. Usually a system of 


fringes will be seen. Let us suppose that there is a certain line 


across the large plate at all points of which the large plate is 


thicker than the small piece by a constant amount. If the little 


square is moved along this line, the fringe produced by the dif- 


ference in thickness will remain in a fixed position. But it is 


assumed that we do not know where this line is, and we wish to 


trace it out. To do this, choose one of the fringes which is 


bright and easily seen. Then by trial, move the small square a- 


cross the large sheet so that this particular fringe remains 


fixed in position. The small glass thus traces out a contour line 


of tne large sheet at all points of which the large sheet has a 


constant thickness, By this method, a whole system of contour 


lines may be mapped out tor the entire area of the large sheet 


of glass, 


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VI. The Michelson Interferometer. 


Some very accurate measurements have been and can be made py 
the simple methods of producing interference already described, 
but the instruments of greatest precision which are based upon 
the principle of interference are known as interferometers. The 
best known and most widely used interferometer is that devised by 
Professor A, A, Michelson of the University of Chicago, It was 
originally designed by him for use in a very famous experiment 
to determine the ether drag or drift, which he and Morley per- 
formed, an account of which was published in 1886. The most con- 


mon form of this in- 


adivitoenkél strument is shown in | 
12 Figure 18. Suppose 
that we have a source | 
of monochromatic light 


S, say a sodium flame, 
[\ oe passing through a lens 
K? YY L which renders the | 
y AGC Ci rays of light parallel | 
These rays strike a 
Figure 18, glass plate M at an 
angle of forty five degrees and are transmitted through it to the 
half silvered surface AB, Here half of the light is reflected to 
the mirror P which is heavily silvered on the front surface. This 
light is then reflected directly back to M and is transmitted 
through to the eye. The other half of the light passes through 
the half silver film to the mirror 0 which also reflects the light | 
directly back to M where the half silvered film reflects it to 


the eye, Thus the eye receives wave trains which have passed over 


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two different paths, one trom M to P and back, the other from M 
to 0 and back, These paths will hereafter be designated as MPM 

and MOM. From the figure, it is seen that any ray of light from 
S which is reflected by the half silvered film up to P and back 


again to the eye must pass through the glass plate M three dif- 


ferent times, Also any ray which passes through to 0 and pack and 
is then reflected to the eye, passes through M only once. Hence 
the ray MPM passes through three times as much glass as the ray 
MOM, and this will mean a large difference in the optical path of 
the two rays of light. To compensate for this, another plate of 
Slass C, known as the compensator, is placed in the path of the 
ray from M to O and back. This plate is not silvered on either 
Side, but it is cut from the same piece of worked glass that M is 
cut from, hence it has the same thickness. It is set on the sup- 
port in the same angle as M, so that the ray MOM travels through 
exactly the same thickness of glass as the ray MPM. The mirror P 
is rigidly mounted on a heavy steel slide which is made to slide 
along very accurately ground steel ways by means of a long screw 
having a pitch of one millimeter. To the end of this screw is 

attached a steel disk of four or five centimeters diameter, its 
edge being marked off into 100 equal divisions. Thus, when the 

screw has made one complete turn, the mirror P has moved either 
forward or backward a distance of one millimeter. By means of the 
graduations on the disk, the screw may be made to turn through 
.Ol of a turn thus moving the mirror .01 of a millimeter. The 

screw may be turned quite rapidly by a small crank at the end. 

But in addition to this, there is attached to the screw as an 

axis a worm wheel in the teeth of which a worm screw can be en- 


gaged at will. By turning the worm screw by means of a milled 


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head, the large screw can be turned very slowly. When the worm 


Screw has made one complete revolution, the large screw has passed 


through .O1 of a turn. The worm screw is also equipped with a head 


which is divided into fifty equal parts. therefore when the worm 


A 


screw has moved through a distance equal to one half of one of 


these divisions, the mirror P has moved through a distance of .001 


millimeter, Therefore, we can measure the distance through which 


P moves very accurately to thousandths of a millimeter, and by 


estimating tenths of a division, readings to one ten-thousandth 


of a millimeter may be made, When the screws are clean and in good 


condition, so that there is no lost motion, this type of inter- 


ferometer is one of the most accurate instruments of measurement 


known, The plate M is held in a metal frame whicn is rigidly at- 


tached to the base plate, The compensator C is held in a metal 


frame which can be turned through a small angle so as to keep 


C adjusted parallel to M. The mirror O is held by springs against 


two adjusting screws which are set in a vertical plate immediately 


behind 0. These screws are used to get the instrument in adjust- 


ment so that the fringes may be seen. 


How are uhe fringes produced with the iiichelson interferom- 


eter? When the mirrors 0 and P are rigorously perpendicular to 


each other and are poth the same distance from the silver film 


AB, the image of O in AB wili coincide with P. But if they are 


not exactly perpendicular, tne reflected image of 0 will form a 


very small angle with P tnus producing a condition similar to 


that of the air wedge described on page 16, Figure 11, and in- 


terference fringes will be seen, If the mirrors are not exactly 


vertical, fringes will appear again, but whey will be perpen- 


dicular to those formed when the mirrors are not perpendicular. 


4' 


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Again, if the two mirrors are unequal distances from AB, then the 
rays of light will converge from ali points of tne mirrors as they 
come nearer the eye, and the paths of the different rays will 
therefore be of unequal lengths, ana there will be interference, 
this time in tne form of circular fringes. Thus we may see ver- 
tical, horizontal, or circular fringes depending upon the relative 


positions of the two mirrors O and P, 


Let us consider for a moment a particular bright fringe seen 


in tne field. We know that for this fringe, the paths traveled by 
the two rays of light MOM and MPM are such that the rays reinforce 
each other, Now if the mirror P is moved forward a very small dis- 
tance, the length of the path MPM has been so changed that tne 
wave train passing over it now interferes with the wave train 
passing over the path MOM, and we have a dark band where there 
was a bright one before. But the bright fringe has not disappeared. 
It has simply moved across the field a short distance, Thus, as 
the mirror P moves forward or backward, the tringes are seen to 
move across the field, If they are circular fringes, they will 
expand from the center if P is moving away from M, and will con- 
tract toward the center if P moves towards M. This fact is made 
use of in many experiments done with the interferometer some of 
which will now be described 

VII. Some Actual Experiments Using The Interferometer, 

A few experiments as actually performed with the interfer- 
ometer will be described here, 

1. Adjustment of the interferometer: In the more common ex- 
periments performed with the Michelson instrument, a sodium 
flame is generally used as the source of monochromatic light. 


A convenient method of producing such a flame is to take a square 


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a AN 
piece of filter paper and roll it into a tube just large enough 


to slip over the tube of a Bunsen burner, Wrap the paper tube with 
ordinary grocer's twine so that it will hold its shape and then 
Soak the tube in a solution of common salt. After soaking, it is 
allowed to dry. It may then be slipped over the Bunsen burner so 
that the edge of the paper projects a small distance above the 
mouth of the burner, When the burner is lighted, the paper burns, 
and the salt causes the flame to be a bright yellow which is the 
sodium flame. A paper tube made in this way will produce a sodium 
flame for several hours. 

Now set up a convex lens between the flame and the plate M 
of the interferometer, placing the flame so that it will be in the} 
focal point of the lens. (Figure 13). Wave trains coming trom the | 
flame will thus be rendered parallel by the lens and will strike 
the mirror M in parallel lines. By means of a small piece of wax, 
stick a pin to the lens, so that the point projects down into the 
path of the light coming from the flame. The mirrors 0 and P 
Should be as nearly as possible the same distance from M, The dis-. 
tance of O from M may be roughly measured by means of a meter 
Stick, and P may be moved by means of the screw until it is the 
Same distance from M. Then by placing the eye in the position 
shown in Figure 18, four images of the pin will be seen as shown 

in Figure 19. Two of the images will be quite 
| plain, and two will be dim. By means of the 
two adjusting screws at the back of 0, it may 
Figure 19, be moved through a small angle so that the 
dim images of the pin will coincide exactly with the darker in- 
ages, When this coincidence takes place, the fringes will appear. 


Then by a few adjustments of the screws, they may be made circu- 


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lar, horizontal, or vertical as desired, and their width may also 
be varied, 

2, Measurement of the wave length of sodium light. 

The wave length of light is usually measured in Angstron 
units, Such a unit is defined as being equal to 10. centimeter, 
or ,Q00000001 centimeter. 

Let us tix our attention upon one particular bright fringe 
in the field of view, Now if we move the mirror P forward so that 
the fringe has been displaced, and the next adjacent bright 
fringe has moved into its place, then the difference in path be- 
tween the two rays MOM and MPM has been changed by one whole wave 
length. This is equivalent to saying that the path MPM has been 
Shortened one whole wave length. But the light is traveling over 
the path from M to P, and then back to M, or in reality, it passes 
twice over the same path. Hence to change the path one whole wave 
length, the mirror P moves through a distance of only a half wave 
length. Now by means of the small worm gear and screw, the mirror 
may be moved forward slowly. During this motion, count the fringes | 
which pass a given point in the field of view. Let us say that 
100 fringes have passed across the field. We may read tne distance 
through which the mirror has moved from the graduations on the 
head of the screw. This distance multiplied by two and divided by 
100 gives the wave length or the light used, The following re- 
Sults were observed for a sodium flame. The column headed D gives 
the distance in centimeters through which the mirror P moved, The 
next column gives the values of 2D, the third colum, N, gives 
the number of fringes counted, and the fourth column headed 1, 


gives the wave length which is gotten by use of the equation 


1 = 2D/N (8) | 


int 


_ : 
: eet i doug : barns iq 


y ‘¥ 
mt 


é.le a IO 


: @ “ 


The fifth column gives 1 in Angstrom Units. 


D 2D N 1 (2D/N) 1 
,002950 005900 100 ,00005900 5900 
002963 005926 100 00005926 5926 
002935 005870 100 00005870 5870 
.002946 .005892 100 .00005892 53892 
.002945 005890 100 00005890 5890 


The average of these results is 5895.6 Angstrom units. Sodium 
light consists of waves of two slightly different lengths. The 
wave length of the shorter sodium waves is generally given as 
5890.22 Angstrom units, and for the otner component, the wave 
length is 5896.18 Angstrom units. Thus it is seen that the value 


obtained above agrees very closely. with the generally accepted 


values, 


In order to get accurate results in this experiment, care 
must be taken that all lost motion of the screw is taken up be- 
fore counting of the fringes is begun. Any lost motion will in- 
troduce considerable error. This is not a difficult experiment 
to do once the interferometer is adjusted so that the fringes 


are sharp, It is however rather tedious, and is very tiring to 


the eyes, 


3. Ratio of the wave length of the D lines. 


The fact was brought out above that sodium light is com- 
posed of two different wave lengths. When sodium light is allowed 
to pass through the slit of a spectroscope, the prism refracts 
these two different wave lengths through slightly difierent an- 
&les, so that two yellow lines are seen, These lines are know 


as the D lines, the one having the longer wave length being the 


Di line, and the other the Dz line. Let the wave length of the 


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D1 line be 11, and that of the Dz line be lz. The interferometer 
furnishes a means of determining the value of the ratio +s ; 

The theory is as follows: Suppose that the paths of the two 
wave trains of light in the interferometer are exactly equal, and 
that the light is coming from an absolutely homogeneous source, 
that is, a source which sends out waves of one definite wave length 
only. This set of waves will produce only one set of fringes, and 
in this case, the mirror P may be moved any distance without de- 
Stroying the fringes. But such a source of light is very difficult 
to realize or obtain, If sodium light is the source, we have two 
different wave lengths producing fringes. Now when the two paths 
MOM and MPM are equal, or in other words, when the difference in 
path is zero, then the fringes formed by one wave length will co- 
incide with those of the otner wave length. But as the mirror is 
moved, or the difference of path is changed, both sets of fringes 
will move across the field of view, but one set will move across 
the field more rapidly than the other, When the difference in 
path has been increased the proper amount, one set of fringes will. 
have gained on the other set by half a fringe, which means that 
the fringes of one set will occupy the dark spaces between the 
fringes of the other set. When this occurs, if the intensity of 
the light for both sets of waves is the same, the fringes will 
disappear, because one set completely illuminates the dark spaces 
between the other set, But if they are not of the same intensity, 


then both sets of fringes may be seen, but they will both be 


dimmed. Now when one set has gained half a fringe on the other, 
the difference in path of MPM and MOM contains half a wave length 


more of the shorter waves than the longer ones. That is, if the 


difference in path contained 1000 of the longer wave lengths, it 


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would contain 1000.5 of the shorter ones. Let N be the number of 


Di waves of length licontained in the difference of path, The 
difference of path will then be equal to Nli. Let N + .5 be the 
number of Dz waves of length lz contained in the same path dif- 
ference. Then the path difference is also equal to (N + ,5)l2 
Therefore we may write 
Naw Ny + ode | (9) | 
But to produce any given difference of path, we have seen that the | 


mirror P moves through only half that distance, Then 


Nl1 = (N ats a il2 (10) 


2 2 
Dividing through by lz, we have 


Nii El (N+ ,5) 
Bay te 2 


And dividing through by N/2 gives 
2s ae a a 
12 N 


which gives the ratio of the wave lengths of the two D lines of 
sodium light. In the actual manipulation of the experiment, the 
difference in path is made zero by moving the mirror P toa 
position where it is the same distance from M that 0 is. The two 
sets of fringes are then coincident and brightest, Then move P 
Slowly either forward or backward, until the fringes disappear 
or are dimmest, counting the fringes which cross the field during 
the movement, The number counted will give the value which must 
be substituted for N in the equation above to give the value of 
the ratio li/ 12. 
The following results were observed: 
N Tey yates 


aO'7 


‘ 


1.001006 


a 


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E) of faupetonsa af oem 4T tb pte aly 
ae a, 
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nadT .oomibey add Diam Metingnel 


bor ah 
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aor cali my. 


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cir) Rasp a 


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he 

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h 
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s00200. 17 

yy ue 


1.000991 


1.001020 
1.001022 


1.001014 
1.000988 


1,001026 


1.001004 
1.001002 


491 1.001018 


The mean value of these results gives li/ lz = 1.0010091. If we 


take the wave length of the Dz line as 5896.18 and of the D, line 


as 5890.22, we have Tea 5896.16." " 2 
7 eter eo 7 1.0010101 


These two results vary from each other by one part in one million. 


A study of the separate readings however does not show this close 


agreement, This discloses the fact that there are some diffi- 


culties in making the experiment. The chief difficulty is in the 


inability of the eye to tell when the fringes are dimmest, in 


other words, when there is least visibility. This is shown in 


the marked variation in the values of N. Another difficulty lies 


in the fact that as the position of lowest visibility approaches, 


the fringes become so dim that they are exceedingly difficult to 


count, Hence the desirability of taking a large number of read- 


ings by which the errors in some will counteract the errors in 


others, 


The value of the interferometer in spectroscopic work is 


not so clearly demonstrated by this experiment as it is by the 


inversion of this process, If, when light passes through the 


S 


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interferometer, this change in the visibility of the fringes oc- 
curs with the change in path difference, then we may be sure that 
the source is composed of waves of difirerent wave lengths, Thus, 
the interferometer is of great value in spectroscopic work in 
analyzing the various lines of the spectrum into their components. 
Some of the lines are much more complex than the sodium line, and 
are made up of a number of different wave lengths. But Michelson, 
with his interferometer and with a machine of his own design 
called the harmonic analyzer, has done some very noted work in 
separating lines of the spectrum into their components, which 
could not be separated by the best of grating spectroscopes. His 
harmonie analyzer is a machine which automatically draws what are 
known as "visibility curves" for the various spectral lines as 
they are seen through tne interferometer, A study of these curves 
shows the composite character of the lines, buu it takes one 
expert in the method to get the full meaning from the curves, 
The method is more fully described in Michelson's book entitled 
Light Waves And Their Uses, The Michelson interferometer however 
is not so well adapted to spectral analysis work as the Fapry- 
Perot interferometer which will be described farther on, and its 
advantages in this kind of work will be then pointed out. 

4, Measurement of the index of refraction, 

We have already seen that the rringes formed by two different 
wave lengths overlap each other for a certain path difference. 
If the source is white light, we have all colors of the spectrun, 
or all the wave lengths from the longest to the shortest, The 
fringes formed by all these different wave lengths will coincide 
when the path difference is zero, but when the mirror P is moved 


in either direction, the shortest wave lengths soon gain half a 


nel 


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fringe over the longest, and the fringes disappear entirely. This 


will happen when the mirror is moved a very small fraction of a 
millimeter. The appearance ot white light fringes therefore fur- 
nishes a very accurate means of telling when there is no differ- 
ence of path, or when MPM and MOM are equal. Let the interfer- 
ometer be adjusted for white light fringes. Now if a glass plate 
is placed in the path MPM, the effect is to increase the path as 
if the mirror P had been moved away from M, and the fringes will 
vanish, Now if the mirror is moved toward M, the path will be 
shortened, and when the decrease in path thus caused is equal to 
the increase previously caused by the glass plate, the white 
light fringes will reappear, Now the velocity of light through 
glass is slower than it is through air. If the velocity in glass 
is V2, and in air Vi, the velocity in glass is kh/ Vitimes Vi. 
This decrease in velocity corresponds to an optical path of 

Vi/ V2times the thickness of the glass. This ratio Vi / Ve is 
called the index of refraction ot the glass, and it may be desig- 
nated as m. Then it the thickness of the glass is t, the optical 
path through the glass is mt. If the glass were not in the path, 
the light would travel through a distance t in air which fills 
the space occupied by the glass. Therefore, the difference in 


path D caused by the glass is 


D=mt-t 


and solving tor m, we have 


D.+ t+ 12 
m (12) 


In the manipulation of this experiment, the interferometer | 
is first adjusted for white light fringes. This is done by setting | 


the mirror P as nearly as possible the same distance from M as 


Se EE Ee 


= GB 
the mirror 0. This may be done fairly weli by simply measuring 


with a meter stick. Then with sodium light, adjust the mirror 0 
by means of the adjusting screws so that the fringes are as dis- 
tinct as they may be made. Now substitute white light for the 
sodium light, and with a slight turn or two of the worm gear 
wheel, the fringes should appear. Now mount the glass plate for 
which m is to be found in the path MPM, so that it just covers 
half of the field. The fringes will therefore disappear over tnat 
half of the field covered by the glass, Now move the mirror for- 
ward slowly, and when the distance moved has shortened the opti- 
cal path as much as tue glass has increased it, the fringes will 
appear again, but this time in the half of the field of view 
covered by the glass, The distance through which the mirror has 
moved may be read Irom the circular scale, which gives the value 
of D in equation (12). The thickness of tne glass, t, may be 
measured accurately by means of a micrometer caliper, or better, 
by means of a spherometer which is graduated to thousandths of a 
millimeter, These values substituted in (12) gives the value of 
mn. 

Two sets of observations are given here, one for a micro- 
scopic cover glass which was .1675 millimeter thick, and the 
other for an interferometer plate which was 2.1536 millimeters 
thick. The values of D are also given in millimeters, 


For the microscopic cover glass: 


D t m= DLL 
0904 1675 1,539 
0979 sG7e 1.584 
~950 GTS 1.567 


951 £1675 1.567 


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0954 wiicg i) 1.570 
0993 ~1675 1.593 
0907 OTS 1,542 
.0910 1675 1.544 


The variation in these results is rather large. This may be due 
in part to the fact that the glass was not of uniform thickness 
througnout which would produce considerable variation in the 
readings, Another precaution wnich is necessary to observe is to 
see that when the white light fringes reappear, that they be 
brought to the same position in tne rield, On their reappearance, 
they are apt to be dimmer and smaller than they were before the 
glass plate was placed in the path, After some practice, they can 
usually be brought very nearly to the same position. Another 
precaution to prevent error is to see that tne plate is perfect- 
ly parallel to the mirror P, If it is inclined to it at a small 
angle, the thickness of glass through which the lignt passes will 
be greater than the measured thickness which is used in tne equa- 
tion. 

The results for tne interferometer plate, which was made of 
very fine glass anda whose surfaces were accurately parallel, show 


much greater accuracy, 


D t 
1.1995 2.1536 
1,1998 Noyes 


1.1930 


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The per cent of variation between the largest and the smallest 


i n= DEt 
1.1901 2.1536 1,552 
1.1959 2.1536 1,555 
1.1996 2.1536 1.557 | 
1.2016 2.1536 1.558 | 
1.2007 2.1536 1.558 | 
1.1973 2.1536 1.555 | 
1.1989 2.1536 1.556 | 
| 
| 


value of m given above is ,38 of 1 %. These results are very con- 
Sistent, so the mean result snould give a very close value of m 
for this particular plate. 

This method has been used to measure the index of refraction 
of various liquids and gases, and to show the change in m of a 
gas under varying pressures, The gas or liquid may be placed in 
a tupe with glass ends, and the tube is then placed so that the 
ray MPM must pass through the tube, This causes a displacement of 
the white light fringes in the same way as the glass plate, and 
the calculations are very similar. 

VIII. Some Famous Classical Experiments. 


Consider again the equation 


and solve it for t. Then 

teaB, (13) 
This equation suggests a method of using the Alvear HAE 
measuring tne thickness of transparent substances, The procedure 
is similar in every way to that given above for determining ao, 
but in this case, m is a known quantity, and t is tne unknown. 


Since with the interferometer we are dealing with light waves 


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wnich have a very small length indeed, this method lends itself 


admirably to the measurement of very thin plates, such as the film 
of silver on a mirror or a soap film, 


E, S. Johonnot, in an issue of the Philosophical Magazine 


| 


of 1899, reported the results of an experiment in which he measured 
the thickness of the black spot of a soap film. He found that one | 


Soap film placed in tne path of one of the interfering wave trains 
produced no appreciable displacement of the tringes. He therefore 
constructed a frame by means of which he could place as many as 
fifty soap rilms in a row in one path, and this produced a dis- 
placement of halt a fringe. Johonnot calculated that when the 
film was thin enough to show the black spot, that it musu not be 
composed of more than two layers of molecules, Therefore he took 
his measurement of che thickness to be the upper limit to the dis- 
tance between the molecules of the substance. He showed the thick- 
ness of the film at its thinnest part to be about six millionths 
of a millimeter. 

Michelson has made very good use ot wune interferometer in 
measuring very small angles which could not be measured in any 
other way. He has also used it to measure the coefficient of ex- 
pansion of substances which could not be obtained in large enough 
bodies to make their expansion appreciable by any other method, 
The interferometer has also been used in connection with a very 
delicate balance by which the gravitational force exerted by a 
large lead ball upon a small one could be measured. The force to 
be measured was about one twenty millionth of the weight of the 
small lead ball, a force which could not be measured by an or- 
dinary balance even when a microscope was usea in connection with 


it. The interferometer has also been used to test the accuracy of 


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very fine screws such as those used in dividing engines with 
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which fine diffraction gratings are ruled. Such a screw must b 


Aside from these valuable uses which Michelson has made of 


very accurately turned, 
the interferometer, he has performed what may be termed some very | 


Startling experiments with it. He has measured the diameter of the | 
great star Betelgeuse disclosing the fact that it is a heavenly 


body the size of which is beyond the power of the most vivid 


re 


imagination to conceive. One of Michelson's most famous experi- 
ments is that in which he determined the length of the standard 
meter in Paris in terms of the wave lengths of the red, blue, and 
green spectral lines of cadmium. By an ingenious modification of 
the interferometer, he succeeded in getting very accurate and 
consistent results. The readings were taken by Michelson and two 
other observers, and at wide intervals of time from each other, 
which makes the very consistent results which they obtained even 
more convincing. They found that the number of light waves in a 
standard meter was, for the red cadmium line, 1,553,163.5, for 
the green, 1,966,249.7, and for the blue, 2,083,372.1. They found 
that the absolute accuracy was about one part in two million, 

One of the most important and interesting problems which 


many eminent scientists have attempted to solve is that of the 


ae 


"ether drift", It was pointed out in the early part of this dis- 
cussion that there must be a medium by which light waves may be 
transmitted through space, This medium is known as the ether and 
it is characterized as an elastic solid. The problem of the 
"ether drift" is the question of whether the ether is carried 


along through space with the earth as it moves through its or- 


bit about the sun, or whether the ether remains stationary with 


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respect to the earth, It was in an effort to solve this problem 
that Michelson iaventiee he interferometer, In performing this 
experiment, he had the collaboration of Morley, and the results 
of their experiment were published in the Philosophical Magazine 
in 1887. An interferometer was built on a rather large scale. It 
was mounted on a stone which was about four feet square and one . 


foot thick, and this stone was mounted on a block of wood which 


rendered the instrument free from all minor vibrations and made 


| 
was floated in a tank containing thirteen tons of mercury, This 
it possible to turn the interferometer through an angle of ninety 


degrees witnout getting it out of adjustment. Light coming from 


the source was divided by a half silvered mirror into two beans 


at right angles to each other, and these beams were reflected 


back and forth several times between a series of mirrors mounted 


at the four corners of the stone, By this large number of reflec- 


tions, the beams were made to travel over a path of about ninety 


feet, The beams were finally brought together again and reflected 


into a telescope where they were in a condition to interfere, and 


interference fringes were produced. Michelson predicted that if 


the ether did not move with the earth through its orbit, there 


would be a displacement of half a fringe when the interferometer 


was rotated through ninety degrees. The instrument was set so 


that one of the beams of light was in the direction of motion of 


the earth in its orbit, and the other beam was at right angles 


to this motion, Then when the interferometer was turned through 


an angle of ninety degrees, the two beams were interchanged with 


respect to the motion of the earth, If the ether were stationary, 


this would cause a retardation of one beam behind tne other so 


el a A = ae Ae 


7. 
: 


pa: ae 
as to cause the displacement of fringes. The observations were 
taken at different times covering a period of a year so as to make 

sure that the motion of the earth was not in any way affected : 
by the attraction of any other heavenly body. The predicted dis- | 
placement of the fringes however was not observed. The natural | 
conclusion to draw from the results is that the ether moves along | 


with the earth in its orbital motion, but there have been some 


other hypotheses suggested to explain the negative results ob- | 
tained. One of them is based upon tne theory of relativity which | 
assumes that a body in motion is shortened if its length lies in : 
the direction of motion. If this theory is true, the beam of 

light lying in the direction of motion of tne earth's motion 

would travel over a shorter path because of the shortening of the 
apparatus in that direction which would account for the results 
which Michelson and Morley obtained without discrediting the 
theory of the ether drift. Michelson has been working on the 
problem during the last year (1921), and it is hoped that the 
results obtained from his more recent work will throw consider- 
able light upon the whole subject of the theory of relativity. 

IX. Other Types Of Interferometers, The Fabry-Perot, 

Next to the Michelson interferometer, the most widely used 
instrument is the Fabry-Perot interferometer, It is very simple 
and consists essentially of two plates of glass, each one being 
half silvered on one surface, The plates A and B (Fig. 20) are 
mounted on a support so: that their 
Silvered surfaces are facing each 


other. We shall first suppose that 


the two plates are not exactly 


Figure 20 parallel to each other. Let S be 


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avery narrow slit illuminated by monochromatic light, The light 
will pass to the two plates, and part of it will be transmitted 
directly to the eye. Another part will be reflected at o back to 
p, where it will be reflected again back to r, Here a part will 
be transmitted to the eye, while another part will again be re- 
flected to s and then back to t. These reflections between the 
plates will be numerous, and the eye will see a number of images 
of the slit arranged side by side and parallel to the real slit. 
Now if the mirrors are adjusted so as to be parallel to each other, 
these images will all coincide with each other, But the light 
which reaches the eye from the first image has traveled over a 
path which is shorter than the path of the light from the second 
image by a distance equal to twice tne distance between the plates, 
Similarly, the light from the second image has traveled a short- 
er distance than that from the third, and so on, The wave trains 
from these images are therefore in a condition to interfere if 
the plates are parallel. When they are very nearly parallel, the 
fringes will be straight and very fine and narrow, As exact par- 
allelism is approached, they will become wider, and when the 
plates are exactly parallel, they will be circular, Due to the 
large number of reflections, the fringes are very narrow, and 

the dark bands between are very wide. This constitutes an ad- 
vantage over the Michelson instrument especially in spectroscopic 
work; It was mentioned on page 40 that when the source of light 
for the Michelson interferometer is of a composite character, 
there are points or positions of the mirror P at which the 
fringes caused by one wave length fill the space between the 


fringes due to the otner wave length, and in this case, the 


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fringes become very dim or else disappear entirely. For this 
reason, it is very difficult to determine the position of the 
mirror P for which the visibility of the fringes is lowest. But 
with the Fabry-Perot instrument, as just pointed out, the dark 
space between the fringes is very wide compared to those of the 
Michelson interferometer. Therefore when light of two different 
wave lengtns is used ana the shorter one has gained half a fringe 
over the longer one, the fringes of the shorter wave lengtn 
Stand out very clearly in the spaces between the fringes of the 
otner wave lengtn. Hence the value of N in equation (11), page 
38, can be much more accurately deteimined with uhe Fabry-Perot 
interferometer. 

In using this instrument, the light is generally passed 
through a prism first, and only light from one line of the spec- 
trum thus produced is allowed to pass tnrough the plates, which 
makes the light as nearly monochromatic as possible, The adjust- 
ments necessary to see the fringes are however very tedious, and 
it requires considerable practice and patience to become accus- 
tomed to the instrument. 


2. Jamin's Refractometer. 


The interferometer devised by Jamin was made especially to 
measure the index of refraction of gases and liquids, and is 
therefore most commonly 
spoken of as the refrac- 
tometer, It is based 
upon the principle of 
interference by thick 


plates as explained on 


page 26. Two plates of 


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parallel surface glass of equal thickness, usually about one cen- 


timeter, are mounted parallel to each other on an optical bench 


as shown by AB ana CD in Figure 21, The plates are mounted ver- 


tically, so that in the diagram, they are shown as perpendicular 


to the plane of tne paper. Each plate is silvered on its back 


i 
surface, Light from a source S passes through a lens which causes | 
@ parallel pencil of rays or wave trains to fall upon the plate | 


AB at O at an angie of forty tive degrees, Part of this light is 


reflected from the front surface over to the point P at the front 


surface of the second plate. It is here transmitted to the back 


Surface where it is reflected downward at Q and emerges from the 


plate at R. A second part of the light from S upon striking AB 


at 0 is transmitted to the back surface where it is reflected at 


M to N of the front surface and thence to R on CD where it is re- 


flected again. Thus the beam trom S is divided into two beams as 


they pass through and between the plates only to be reunited a- 


gain as they leave the second plate at R. Now if AB and CD are 


rigorously parallel to one another, the paths ot the two beams 


will be equal to each other, and the beams will emerge at R in 


the same phase and therefore in condition to reinforce each other. 


In this case, the field of view will be uniformly illuminated, 


provided the plates are perfectly plane. But suppose that the 
plate CD is inclined to AB by a very small angle. Then the path 


of the wave train OPQR will be slightly different from that of 


OMNR, and they will emerge at R in opposite phase causing inter- 


ference fringes to appear in the field of view, The plate CD is 


mounted in such a way that it can be controlled by two screws, 


one of which moves it about a vertical axis while the other moves 


it about a horizontal axis. These screws are graduated so that 


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the angle through which the plate moves can be read directly from 


the instrument. If the instrument is adjusted so that the fringes 
are seen, and a piece of glass is then placed between the plates 
and in the path of only one of the beams, this beam will be re- 
tarded by the glass, and the fringes will be displaced a certain 
amount as the result. Jamin made use of this fact to measure the 
index of refraction of various gases. He placed a tube contain- 
ing a gas, the index of refraction of which he wished to deter- 
mine, in the path of one of the beams, say OP, (Fig. 21) which 
retarded that beam a certain amount behind the beam NR thus 
causing a displacement of the fringes. Now by putting a piece of 
glass of the proper thickness in tne path of the beam NR, it 
could be retarded an equal amount, so that the fringes would be 
returned to their original position, or if tube and glass are 
placed in position at the same instant, the fringes would not be 
displaced at all. Then, the index of refraction of the glass be- 
ing known, the retardation which it causes can be calculated. 
This will be equal to the retardation caused by the gas in the 
tube, and from this fact, ius index of refraction may be deter- 
mined, The glass used (G in Fig. 21) is known as the compensa- 
tor. It is evident that for different gases, the compensator 
would have to be of different thicknesses, It would be a very 
tedious process to try one piece o1 glass after another until 
one of the right thickness was found. Jamin's original compen- 
sator consisted of a single piece of 
glass mounted upon a vertical axis, 
By turning the plate on its axis through | 
an angle, the thickness through which 


Figure 22. 


the light passes could be varied as | 


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much as desired, A better form of compensator is illustrated in 
Figure 22, It consists of two very slender prisms whose angles 
are equal, and which are placed one upon the other so that their 
edges are opposite each otner. In such a position, they form a 
parallel plate, and by means of a screw, one prism may be slid 
along the otner thus varying the thickness of the plate at will. 
Such a compensator can be calibrated for the various relative 
positions of the two plates, and when calibrated, it is very use- 
ful in making experiments with the Jamin refractometer. 

3. Lodge's Interferometer. 

The principle of the Lodge interferometer is easily under- 
Stood by a study of Fig- 
ure 23. Three glass plates 
AB, C, and D are used and 
set up as shown. The 
plates C and D are in- 
clined to AB at an angle 
of forty five degrees. 
The plate AB is half sil- 


vered on the surface next 


Figure 23. to the source of light 5. 


C and D are heavily silvered on their front surfaces, Light from 


the source S strikes the half mirror AB at P. Part of it is re- 


flected and passes along the sides of a triangle between AB, D, 


and C as shown by the arrows. The ouner part is transmitted 


transmitted through AB at P and passes around the same triangle 


but in tue opposite direction. Both wave trains, after passing 


around the triangle in opposite directions, emerge in the same 


direction at 0 in a condition to produce interference. The fringes)! 
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are seen by the eye through a very small opening such as a pinhole, 
or elseby means of a telescope, When C ana D are exactly the same 
distance from the half silvered surface of AB, the reflected in- 
age of C will appear to the eye to coincide with D, Now if C is 
moved forward a very small distance, there will be a virtual air 
wedge between the image of C and the actual surface of D. Inter- 
ference is thus caused in exactly the same manner as with the 
Michelson interferometer, and the fringes formed will be either 
circular, vertical, or horizontal depending upon the angle be 


tween the two mirrors C and D. Lodge used his interferometer in 


an experiment to determine if there is an ether drift. He mount- 


ed the instrument betweentwo circular steel plates of large diam- 
eter which were whirling as rapidly as they could be made to 
whirl without tlying to pieces, If the ether was given a motion 
by tne spinning disks, Lodge predicted tnat there would be a dis- 
placement of the fringes seen in his interferometer, because the 
velocity of the light would be accelerated in one path and re- 
tarded in the other by the moving ether. But after all spurious 


effects were done away with, there was no displacement of the 


fringes observed. The conclusion was that there was no drag of 
the ether along with the moving body, at least in tne case where 
such a small moving body was used. 


There are still other types of interferometers which might 


be described here, but they are all based upon principles very 
Similar to those already described here, and none of them is as 
widely used as the Fabry-Perot and Michelson instruments. One 
interferometer manufactured by Ph, Pellin of Paris is known as 
the Fizeau instrument. It makes use of tne principle of Newton's 


rings, and is principally used as a dilatometer, Another inter- 


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ferometer due to Lummer and Gehrke is similar in principle to 
the Fabry-Perot instrument except that the multiple reflections 
are made to take place between the two surfaces ot a single plate 
of glass rather tnan between adjacent surfaces of two separate 
plates, 

X, Conclusion, 

Books might be written upon the subject of interterence and 
its applications and measurement without going over the same 
material twice. It is hoped that what has been presented here 
will acquaint the reader with the elementary principles and 


applications of the interference o1 light, and that a desire 


may be kindled in him to explore further this interesting frield 


of Science. For further reading on the subject, the following 
books are recommended: 

Michelson - Light Waves And Their Uses. 

Maclaurin - Light. 
For the more theoretical aspects of the subject, tne following 
are good: 

Hdser - Light For Students. 

Preston - The Theory Of Light. 

Wood - Physical Optics, 
For directions as to performing various experiments in inter- 
ference, see - 

Clay - Treatise On Practical Light. 

Mann - Applied Optics, 
The original works of Young and Fresnel are very interesting for 
the light which they throw upon the history of interference and 


of the wave theory of light. 


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=O" = 
I wish to acknowledge my indebtedness to Dr. W. F. Schulz 
of the Department of Physics of the University of Illinois for 
many valuable suggestions given and for his interest in the work 
of preparing this thesis; also to Professor A, P, Carman, head 
of the department, who suggested the topic and gave me much en- 


couragement during the progress of tlhe work. 


UNIVERSITY OF ILLINOIS-URBANA 


VIIA 


3 0112 101352885 


